It means, that if one state begins to gain in power relative to its neighbors, other states should either increase their own power to balance it, or (and more likely) should band together into alliance(s) to counter the threat.

It is not a matter of whether you like your new allies.
Nebulousabstracts such as humanitarian issues cannot interfere (not that I necessarily disapprove of considering such issues in decision making - that is a discussion for another node). Power, force, threat, and leverage are the issues that you focus on - no more and no less.

IMO, the British have usually used this well with their Balance of Power philosophy for the European continent. On the other hand, a commonly held academic belief is that realpolitik directly contributed to the conditions that precipitated World War I, from the complex alliances that "naturally" evolved from the rise of a strong, unified Germany.

I just wanted to note the origins of the term. Otto von Bismarck, chancellor (in German, Ministerpräsident or Reichskanzler*) of Prussia beginning in 1862, coined the term to refer to blatant power politics. Very much in the style of Cardinal Richelieu of an earlier France, Bismarck deliberately ignored similarities of taste, government, and values in his choice of allies, instead focusing on national interests. This abandonment of principle as a guiding force in foreign policy was both unusual in the context of 19th-century Europe and quite powerful (as ought to be expected of a focus on power).

The term seems to be used most often in the United States today in a derogatory fashion, to suggest that the one so accused lacks principles or strength of character.

I am told by ilteroi that Bismarck's title was actually Reichskanzler. This term does not seem to appear in Diplomacy, but both terms are well-attested by numerous websites. In any case, it certainly seems as though the more direct translation of 'chancellor', which is preferred by many as his title, is Reichskanzler. I am indebted to ilteroi for the correction.